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intagrate x5/2dx=alog( xk)x7/6+x6 (1+xk)

sneha sunil raikar , 15 Years ago
Grade 12
anser 1 Answers
Jitender Singh

Last Activity: 10 Years ago

Ans: 5/2
I = \int \frac{x^{5/2}}{x^{6}+x^{7/2}}dx
t = \sqrt{x}
dt = \frac{1}{2\sqrt{x}}dx
I = 2\int \frac{1}{t(t^{5}+1)}dt
s = t^{5}
ds = 5t^{4}dt
I = \frac{2}{5}\int \frac{1}{s(s+1)}ds
I =\frac{2}{5}log(\frac{s}{s+1}) +constant
I =\frac{2}{5}log(\frac{t^{5}}{t^{5}+1}) +constant
I =\frac{2}{5}log(\frac{x^{5/2}}{x^{5/2}+1}) +constant
k = 5/2
Thanks & Regards
Jitender Singh
IIT Delhi
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